1. Mostakim, R., Batley, R.T., Saha, S. (2025). A Framework Toward Knowledge Transfer Across Heterogeneous and Sparse Datasets for Fatigue Life Estimation of Additively Manufactured Alloys (accepted in International Journal of Fatigue).

2. Chanwook Park*, Sourav Saha*, Jiachen Guo, Hantao Zhang, Xiaoyu Xie, Miguel A. Bessa, Dong Qian, Wei Chen, Gregory J. Wanger, Jian Cao, Thomas J.R. Hughes, Wing Kam Liu (2025). Unifying Machine Learning and Interpolation Theory via Interpolating Neural Networks. (accepted in Nature Communication) (*co-first authors)

3. Saha, S., Guo, J., Park, C., Lu, Y., Batley, R. and Liu, W.K., 2025. Understanding the Effect of Build Direction and Scanning Strategy on the Tensile Response of Additively Manufactured in 625 with Innovative Calibration Strategy. Available at SSRN 5123395. (Link)

4. Batley, R.T., Park, C., Liu, W.K. and Saha, S., 2025. Explainable Hierarchical Deep Learning Neural Networks (Ex-HiDeNN). arXiv preprint arXiv:2507.05498. (Link)

5. Batley, R.T. and Saha, S., 2025. KHRONOS: a Kernel-Based Neural Architecture for Rapid, Resource-Efficient Scientific Computation. arXiv preprint arXiv:2505.13315. (Link)

1. Park, C.*, Saha, S*., Guo, J., Xie, X., Mojumder, S., Bessa, M.A., Qian, D., Chen, W., Wagner, G.J., Cao, J. and Liu, W.K., 2024. Engineering software 2.0 by interpolating neural networks: unifying training, solving, and calibration. arXiv preprint arXiv:2404.10296. (*Co-first authors)

2. Walker, E., Trask, N., Martinez, C., Lee, K., Actor, J.A., Saha, S., Shilt, T., Vizoso, D., Dingreville, R. and Boyce, B.L., 2024. Unsupervised physics-informed disentanglement of multimodal data. Foundations of Data Science, pp.0-0.

1. Huang, O.#, Saha, S#., Guo, J., & Liu, W. K. (2023). An introduction to kernel and operator learning methods for homogenization by self-consistent clustering analysis. Computational Mechanics, 72(1), 195-219.(# equal contributors).

2. Saha, S., Park, C., Knapik, S., Guo, J., Huang, O., & Liu, W. K. (2023). Deep Learning Discrete Calculus (DLDC): a family of discrete numerical methods by universal approximation for STEM education to frontier research. Computational mechanics, 72(2), 311-331. 

3. Park, C., Lu, Y., Saha, S., Xue, T., Guo, J., Mojumder, S., Apley, D.W., Wagner, G.J. and Liu, W.K., 2023. Convolution hierarchical deep-learning neural network (c-hidenn) with graphics processing unit (gpu) acceleration. Computational Mechanics, 72(2), pp.383-409.

4. Zhang, L., Park, C., Lu, Y., Li, H., Mojumder, S., Saha, S., Guo, J., Li, Y., Abbott, T., Wagner, G.J. and Tang, S., 2023. Isogeometric Convolution Hierarchical Deep-learning Neural Network: Isogeometric analysis with versatile adaptivity. Computer Methods in Applied Mechanics and Engineering, 417, p.116356.

1. Huang, Owen, Sourav Saha, Jiachen Guo, and Wing Kam Liu. "An introduction to kernel and operator learning methods for homogenization by self-consistent clustering analysis." Computational Mechanics 72, no. 1 (2023): 195-219. (# equal contributors).

2. Saha, S., Park, C., Knapik, S., Guo, J., Huang, O. and Liu, W.K., 2022. Deep Learning Discrete Calculus (DLDC): A Family of Discrete Numerical Methods by Universal Approximation for STEM Education to Frontier Research. arXiv preprint arXiv:2211.16610. 

3. Tajdari, M., Tajdari, F., Shirzadian, P., Pawar, A., Wardak, M., Saha, S., Park, C., Huysmans, T., Song, Y., Zhang, Y.J. and Sarwark, J.F., 2022. Next-generation prognosis framework for pediatric spinal deformities using bio-informed deep learning networks. Engineering with Computers, 38(5), pp.4061-4084. Link

4. Alvi, S.M.A.A., Faiyad, A., Munshi, M.A.M., Motalab, M., Islam, M.M. and Saha, S., 2022. Cyclic and tensile deformations of Gold–Silver core shell systems using newly parameterized MEAM potential. Mechanics of Materials, 169, p.104304. Link

5. Ruvo, T.H., Saha, S., Mojumder, S. and Saha, S., 2022. Mixed convection in an open T-shaped cavity utilizing the effect of different inflow conditions with Al2O3-water nanofluid flow. Results in Engineering, p.100862. Link

1. Mozaffar, M., Liao, S., Xie, X., Saha, S., Park, C., Cao, J., Liu, W.K. and Gan, Z. (2021). Mechanistic artificial intelligence (Mechanistic-AI) for modeling, design, and control of advanced manufacturing processes: Current state and perspectives. Journal of Materials Processing Technology, p.117485. Link.

2. Lu, Y., Li, H., Saha, S., Mojumder, S., Al Amin, A., Suarez, D., Liu, Y., Qian, D. and Kam Liu, W. (2021). Reduced Order Machine Learning Finite Element Methods: Concept, Implementation, and Future Applications. Computer Modeling in Engineering Sciences, 129(1). Link.

3. Saha, S., Kafka, O.L., Lu, Y., Yu, C. & Liu, W.K. (2021). Macroscale Property Prediction for Additively Manufactured IN625 from Microstructure Through Advanced Homogenization. Integrating Materials and Manufacturing Innovation, 10(3), pp.360-372. Link.

4. Xie, X.*, Bennett, J.*, Saha, S.*, Lu, Y., Cao, J., Liu, W.K. & Gan, Z. (2021). Mechanistic data-driven prediction of as-built mechanical properties in metal additive manufacturing. npj Computational Materials, 7(1), pp.1-12. (*Co-first authors) Link.

5. Saha, S., Kafka, O. L., Lu, Y., Yu, C., & Liu, W. K. (2021). Microscale Structure to Property Prediction for Additively Manufactured IN625 through Advanced Material Model Parameter Identification. Integrating Materials and Manufacturing Innovation, 1-15. Link.

6. Tajdari, M., Pawar, A., Li, H., Tajdari, F., Maqsood, A., Cleary, E., Saha, S., Zhang, Y.J., Sarwark, J.F., & Liu, W.K. (2021). Image-based modelling for Adolescent Idiopathic Scoliosis: Mechanistic machine learning analysis and prediction. Computer methods in applied mechanics and engineering, 374, p.113590. Link.

7. Faiyad, A., Munshi, M. A. M., Islam, M. M., & Saha, S**. (2021). Deformation mechanisms of Inconel-718 at the nanoscale by molecular dynamics. Physical Chemistry Chemical Physics, 23(17), 10650-10661. (**Corresponding author) Link.

8. Saha, S.*, Gan, Z.*, Cheng, L.*, Gao, J., Kafka, O.L., Xie, X., Li, H., Tajdari, M., Kim, H.A. & Liu, W.K. (2021). Hierarchical Deep Learning Neural Network (HiDeNN): An artificial intelligence (AI) framework for computational science and engineering. Computer Methods in Applied Mechanics and Engineering, 373, p.113452. (*Co-first authors) Link.

1. Tang, S., Li, Y., Qiu, H., Yang, H., Saha, S., Mojumder, S., Liu, W.K. & Guo, X. (2020). MAP123-EP: A mechanistic-based data-driven approach for numerical elastoplastic analysis. Computer Methods in Applied Mechanics and Engineering, 364, p.112955. Link.

2. Islam, K., Saha, S, & Masud, A.K.M. (2020). Molecular dynamics simulation of the mechanical properties of CNT-polyoxymethylene composite with a reactive forcefield Molecular Simulation, 46(5), pp.380-387. Link.

1. Munshi, M.A.M., Majumder, S., Motalab, M. & Saha, S. (2019). Insights into the mechanical properties and fracture mechanism of Cadmium Telluride nanowire. Materials Research Express, 6(10), p.105083. Link.

2. Motalab, M., Paul, R., Saha, S.**, Mojumder, S., Ahmed, T. & Suhling, J.C. (2019). Atomistic analysis of the thermomechanical properties of Sn–Ag–Cu solder materials at the nanoscale with the MEAM potential. Journal of molecular modeling, 25(3), p.59. (**Corresponding author) Link.

1. Saha, S, and Motalab, M. (2018). Nature of creep deformation in nanocrystalline Tungsten. Computational Materials Science, 149, pp 360-372. Link.

2. Paul, R., Tasnim, T., Saha, S.**, & Motalab, M. (2018). Atomistic analysis to characterize the impact of temperature and defects on the mechanical properties of germanene sheet. Materials Research Express, 5, 015062. (**Corresponding author) Link.

1. Rakib, T., Saha, S.**, Motalab, M., Mojumder, S., & Islam, M. M. (2017). Atomistic Representation of Anomalies in the Failure Behaviour of Nanocrystalline Silicene. Scientific reports, 7(1), 14629. (**Corresponding author) Link.

2. Saha, S., Motalab, M.A., & Mahboob, M., (2017). Investigation on mechanical properties of polycrystalline W nanowire. Computational Materials Science, 136, pp.52-59. Link.

3. Rakib, T., Mojumder, S., Das, S., Saha, S., & Motalab, M. (2017). Graphene and its elemental analogue: A molecular dynamics view of fracture phenomenon, Physica B: Condensed Matter, 515, 67-74. 

4. Mojumder, S., Saha, S., Rahman, M. R., Rahman, M. M., Rabbi, K. M., & Ibrahim, T. A. (2017). Numerical study on mixed convection heat transfer in a porous L-shaped cavity. Engineering Science and Technology, an International Journal, 20(1), 272-282. Link.

5. Rahman, M. M., Saha, S., Mojumder, S., Rabbi, K. M., Hasan, H., & Ibrahim, T. A. (2017). Unsteady double-diffusive buoyancy-induced flow in a triangular solar collector shape enclosure with corrugated bottom wall: effects of buoyancy ratio. International Journal of Numerical Methods for Heat & Fluid Flow, 27(6). Link.

1. Mojumder, S., Rabbi, K. M., Saha, S., Hasan, M. N., & Saha, S. C. (2016). Magnetic field effect on natural convection and entropy generation in a half-moon shaped cavity with semicircular bottom heater having different ferrofluid inside, Journal of Magnetism and Magnetic Materials, 407, 412-424. Link.

2. Rabbi, K. M., Saha, S., Mojumder, S., Rahman, M. M., Saidur, R., & Ibrahim, T. A.m (2016). Numerical investigation of pure mixed convection in a ferrofluid-filled lid-driven cavity for different heater configurations, Alexandria Engineering Journal, 55(1), 127-139. Link.

1. Mojumder, S., Saha, S., Saha, S., & Mamun, M. A. H. (2015). Combined effect of Reynolds and Grashof numbers on mixed convection in a lid-driven T-shaped cavity filled with Al2O3 − water nanofluid, Journal of Hydrodynamics, Ser. B, 27(5), 782794. Link.

2. Rahman, M. M., Saha, S., Mojumder, S., Mekhilef, S., & Saidur, R. (2015). Effect of Sine-squared Thermal Boundary Condition on Augmentation of Heat Transfer in a Triangular Solar Collector Filled with Different Nanofluids. Numerical Heat Transfer, Part B: Fundamentals, 68 (1):53 - 74. Link.

3. Rahman, M. M., Mojumder, S., Saha, S., Joarder, A. H., Saidur, R., & Naim, A. G. (2015). Numerical and Statistical Analysis on Unsteady Magnetohydrodynamic Convection in a Semi-circular Enclosure Filled with Ferrofluid. International Journal of Heat and Mass Transfer, 89:1316 - 1330. Link.

1. Rahman, M. M., Mojumder, S., Saha, S., Mekhilef, S., & Saidur, R. (2014). Augmentation of natural convection heat transfer in triangular shape solar collector by utilizing water based nanofluids having a corrugated bottom wall. International Communications in Heat and Mass Transfer, 50:117 - 127. Link.

2. Rahman, M. M., Saha, S., Mojumder, S., Mekhilef, S., & Saidur, R. (2014). Numerical Simulation of Unsteady Heat Transfer in a Half-Moon Shape Enclosure with Variable Thermal Boundary Condition for Different Nanofluids. Numerical Heat Transfer, Part B: Fundamentals, 65(3): 282 - 301. Link.

3. Rahman, M. M., Mojumder, S., Saha, S., Mekhilef, S., & Saidur, R. (2014). Effect of Solid Volume Fraction and Tilt Angle in a Quarter Circular Solar Thermal Collectors 4 of 7 Filled with CNT-Water Nanofluid. International Communications in Heat and Mass Transfer, 57:79 - 90. International Communications in Heat and Mass Transfer, 50:117- 127. Link.

1. Farooq Ghumman, U., Saha, S., Fang, L., Liu, W.K., Wagner, G., & Chen, W., (2020 July) Microstructure Comparison Using Dissimilarity Metric for Additive Manufacturing of Metals. In 2020 International Symposium on Flexible Automation. American Society of Mechanical Engineers Digital Collection.

2. Mojumder, S., Saha, S., Saha, S., Rahman, R. and Saha, S.C., (2020, April). Effect of Magnetic Field on Double Diffusive Natural Convection Inside a Square Cavity with Isothermal Hollow Insert. In IOP Conference Series: Materials Science and Engineering (Vol. 831, No. 1, p. 012010). IOP Publishing.

1. Paul, R., Tasnim, T., Dhar, R., Mojumder, S., Saha, S. and Motalab, M.A., 2017, November. Study of uniaxial tensile properties of hexagonal boron nitride nanoribbons. In TENCON 2017-2017 IEEE Region 10 Conference (pp. 2783-2788). IEEE.

2. Jhumur, N. C., & Saha, S. (2017). Unsteady MHD mixed convection in a T-shaped ventilated cavity filled with ferrofluid (F e3O4 ̆water). In AIP Conference Proceedings (Vol.1851, No. 1, p. 020026). AIP Publishing. Link.

1. Saha, S., Mojumder, S., Mahboob, M., & Islam, M. Z. (2016). Effect of temperature and geometric parameters on elastic properties of tungsten nanowire: A molecular dynamics study. In AIP Conference Proceedings (Vol. 1754, No. 1, p. 030009). AIP Publishing. Link.

2. Mojumder, S., Saha, S., & Saha, S. (2016). Analysis of entropy generation for double diffusive MHD convection in a square cavity with isothermal hollow cylinder. In AIP Conference Proceedings (Vol. 1754, No. 1, p. 050047). AIP Publishing. Link.

3. Saha, S., Mojumder, S., & Saha, S. (2016). Regulation of flow through a T-Shaped open cavity by temperature dependent P, PI, and PID controllers. In AIP Conference Proceedings (Vol. 1754, No. 1, p. 050048). AIP Publishing. Link.

4. Rabbi, K. M., Shuvo, M., Kabir, R. H., Mojumder, S., & Saha, S. (2016). Numerical analysis of mixed convection in lid-driven cavity using non-Newtonian ferrofluid with rotating cylinder inside. In AIP Conference Proceedings (Vol. 1754, No. 1, p. 040016).AIP Publishing. Link.

1. Mojumder, S., Saha, S., Saha, S., & Mamun, M. A. H. (2015). Effect of Magnetic Field on Natural Convection in a C-shaped Cavity Filled with Ferrofluid. Procedia Engineering, 105:96 - 104. Link.

2. Rabbi, K. M., Ahmad, T., Mojumder, S., Saha, S., & Hossain, M. Z. (2015). Geometric Effect on Magnetohydrodynamic Convection in a Half-moon Shaped Cavity Filled with Water Having Semi-circular Bottom Heater. Procedia Engineering, 105:73 - 80. Link.

1. Mojumder, S., Sutradhar, P. K., Saha, S., & Rahman, M. M. (2014). Low head hydropower generation using road side canal water potential in Bangladesh. In the proceedings of 3rd International Conference on the Developments in Renewable Energy Technology (ICDRET), 2014. pages 1-4, Dhaka, Bangladesh, May 29-31, 2014 (doi:10.1109/ICDRET.2014.6861697). Link.

2. Saha, S., Mojumder, S., Rahman, M. M., Mamun, M. A. H., Mekhilef, S., & Saidur, R. (2014). Effect of Lewis Number on Unsteady Double Diffusive Buoyancy Induced Flow in a Triangular Solar Collector with Corrugated Wall. Procedia Engineering, 90:418424. Link.

1. Wing K Liu, Sourav Saha, Satyajit Mojumder, Derick Andres Suarez, Ye Lu, Hengyang Li, Xiaoyu Xie, Zhengtao Gan,

Invention ID: Disc-ID- NU2021-102-01 (Invention disclosure filed on April 21, 2021) Title: HiDeNN: An AI Platform

for Scientific and Materials Systems Innovation (Serial No. 63/177,517)

2. Liu, W.K., Park, C., Saha, S., Mojumder, S., Li, H., Guo, J., Li, Y., Xie, X., inventor; Northwestern University,

assignee. 2023, CONVOLUTION-HIERARCHICAL DEEP- LEARNING NEURAL NETWORK (C-HIDENN) FOR

FAST AND ACCURATE PDE SOLVER AND TRAINER AND APPLICATIONS OF SAME, International application

number PCT/US23/32980.

3. Liu, W.K., Park, C., Saha, S., Mojumder, S., Li, H., Guo, J., Li, Y., Xie, X., inventor; Northwestern University,

assignee. 2023, CONVOLUTION HIDENN-TENSOR DECOMPOSITION FOR MANUFACTURING SIMULATION,

PERFORMANCE PREDICTION, AND TOPOLOGY OPTIMIZATION OF MULTISCALE MATERIAL SYSTEMS, International application number PCT/US23/32981.

4. Liu, W.K., Park, C., Saha, S. et al., Convolution Isogeomertic Analysis for Design/Analysis/Manufacturing, US Pro-

visional patent (63/534,599).

1. Mojumder, S., Saha, S., Rahman, M. M., Mamun, M. M., Mekhilef, S., Saidur, R. A Numerical Study On Effect Of Solid Volume Fraction In Mixed Convection Heat Transfer Phenomena In A Corrugated Bottom Triangular Cavity Filled With Aluminium Oxide Water Nanofluid, 10th International Conference on Mechanical Engineering, ICME 2013.

• Materials Science Science and Technology, Taylor and Francis;

• ECS Journal of Solid State Science and Technology;

• Journal of Materials Research, Springer;

• Computational Mechanics, Springer;

• Materials Research Express, IOP publishing;

• Applied Energy, Elsevier;

• International Journal of Mechanical Sciences, Elsevier;

• International Journal of Automation and Computing, Springer;

• Food and Nutrition, Wiley Online Library;

• International Journal of Numerical Methods for Heat Fluid Flow;

1. Saha, S., Gan, Z., Xie, X., Liu, W. K., Exploring Machine Learning Techniques to Obtain Salient Relationship between Thermal History and Mechanical Properties of Additively Manufactured IN718, 14th WCCM and Eccomas Congress, Paris, France, 11-15 January, 2021.

2. Saha, S., Lu, Y., Liu, W. K., Advanced Identification of Material Law for Micro- and Macro deformation of Additively Manufactured Alloys, USNCCM16, Chicago, IL, USA, 25-29 July, 2021.

3. Saha, S., Gan, Z., Xie, X., Liu, W. K., Mechanistic Wavelet-based Deep Learning (MWDL) for Virtual Experimentation and Classification, MMLDT-CSET, San Diego, CA, USA, 26-29 Sep, 2021 Watch

1. Sourav Saha, Wing Kam Liu, Orion Kafka, Cheng Yu (2020). AFRL Challenge 3: Microscale Structure-to-Macroscale Property Prediction, AFRL AM Modeling Challenge Workshop.

2. Sourav Saha, Wing Kam Liu, Orion Kafka, Cheng Yu (2020). AFRL Challenge 4: Microscale Structure-to-Macroscale Property Prediction, AFRL AM Modeling Challenge Workshop.